The gym is for adults to work out (18+, but sometimes they allow 16+ with a parent). There are no sports courts in the gym.
Not sure if the Triumph has a basketball hoop on the sports deck, but it should have a volleyball court. You may want to ask this on the Carnival board. There should also be ping pong tables. Tip: bring your own sports balls, ping pong paddles/balls to avoid long waits at the purser's desk to check out/check in equipment.